Question

The geometric mean of $6$ observations was calculated as $13.$ It was later observed that one of the observations was recorded as $28$ instead of $36.$ The correct geometric mean is

• A. ${\left(\frac{9}{7}\right)}^{\frac{1}{6}}$
• B. $3{\left(\frac{9}{7}\right)}^{\frac{1}{6}}$
• C. $13{\left(\frac{9}{7}\right)}^{\frac{1}{6}}$
• D. $13{\left(\frac{7}{9}\right)}^{\frac{1}{6}}$

Answer 1

Answer: (C)

Let $x_1,x_2\dots ,x_6$ are the observations and $x_1=28$
$\Rightarrow 28.x_2\dots x_6=13^6$
$\Rightarrow x_2\dots x_6=\frac{13^6}{28}$
Now correct observation is $36$
$\Rightarrow 36.x_2\dots x_6=\frac{13^6}{28}\times 36$
So, now correct geometric mean $=13{\left(\frac{9}{7}\right)}^{\frac{1}{6}}$